Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
r = ?240 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 240 km/h?

v = 240 km/hamax = 2 m/s²
rmin = m
2.Easy
r = 0.8 mv120 rpm

A small object sits 80 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find its centripetal acceleration ac.

n = 120 rpmr = 0.8 m
ac = m/s²
3.Medium
r = 20 mvmax​ = ?

A car takes a flat curve of radius 20 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 20 mμs = 0.4g = 9.81 m/s²
vmax = m/s
4.Medium
r = 150 mvmax​ = ?

A car takes a flat curve of radius 150 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 150 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.5 mv = 7.5 m/s

A 1.9 kg ball on a string 1.5 m long is swung in a vertical circle. At the lowest point it moves at 7.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.9 kgr = 1.5 mv = 7.5 m/sg = 9.81 m/s²
T = N
6.Hard
R = 4 mh = 11.6 m

A 2 kg cart is released from rest at a height of 11.6 m on a frictionless track and runs through a vertical loop of radius 4 m. Use g = 9.81 m/s². Find the normal force Nbottom of the track on the cart at the bottom of the loop.

m = 2 kgh = 11.6 mR = 4 mg = 9.81 m/s²
Nbottom = N

Answer key

  1. 1. rmin = 2222 m
  2. 2. ac = 126.3 m/s²
  3. 3. vmax = 8.859 m/s
  4. 4. vmax = 34.31 m/s
  5. 5. T = 89.89 N
  6. 6. Nbottom = 133.4 N

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